Home
Class 12
MATHS
If f(x)=sum(n=0)^oo x^n/(n!)(loga)^n, th...

If `f(x)=sum_(n=0)^oo x^n/(n!)(loga)^n`, then at `x = 0, f(x)`

A

has no limit

B

is discontinuous

C

is continuous but not differentiable

D

is differentiable

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • CONTINUITY AND DIFFERENTIABILITY

    DISHA PUBLICATION|Exercise Exercise-2 : Concept Applicator|30 Videos
  • CONTINUITY AND DIFFERENTIABILITY

    DISHA PUBLICATION|Exercise Exercise-2 : Concept Applicator|30 Videos
  • CONIC SECTIONS

    DISHA PUBLICATION|Exercise Exercise-2 : Concept Applicator|30 Videos
  • DETERMINANTS

    DISHA PUBLICATION|Exercise EXERCISE -2 CONCEPT APPLICATOR|30 Videos

Similar Questions

Explore conceptually related problems

If f(x)=sum_(n=0)^(oo)(x^(n))/(n!)(log a)^(n), then at x=0,f(x)

Given x in(-1,0)uu(0,1) and f(x)=sum_(n=0)^(oo)x^(n)(-1)^((n(n+1))/(2)) The function f(x) is equivalent to a rational function

If f(x)=lim_(n rarr oo)n(x^((1)/(n))-1) then for x>0,y>0,f(xy) is equal to

If f(x)=lim_(n rarr oo)n(x^((1)/(n))-1), then f or x>0,y>0,f(xy) is equal to : f(x)f(y) (b) f(x)+f(y)f(x)-f(y)(d) none of these

If x = sum_(n=0)^(oo) a^(n), y=sum_(n=0)^(oo) b^(n), z = sum_(n=0)^(oo) C^(n) where a,b,c are in A.P. and |a| lt 1, |b| lt 1, |c| lt 1 , then x,y,z are in

Let x= sum_(n=0)^oo (-1)^n (tantheta)^(2n) and y = sum_(n=0)^oo (costheta)^(2n) qhere theta in (0,pi/4) , then

If f(x)=lim_(n rarr oo)(x^(2n)-1)/(x^(2n)+1) then range of f(x) is

If x=sum_(n=0)^oo a^n, y=sum_(n=0)^oo b^n where |a|<1,|b|<1 then prove that sum_(n=0)^oo (ab)^n=(xy)/(x+y-1)

sum_ (n = 0) ^ (oo) (- 1) ^ (n) x ^ (n + 1) =

DISHA PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-Exercise-1 : Concept Builder(Topicwise)
  1. If f(x)=root(3)((x^4)/|x|) ,x ne 0 and f(0)=0 is:

    Text Solution

    |

  2. Let f:R->R be a function such that f((x+y)/3)=(f(x)+f(y))/3 ,f(0) = ...

    Text Solution

    |

  3. If f(x)=sum(n=0)^oo x^n/(n!)(loga)^n, then at x = 0, f(x)

    Text Solution

    |

  4. If f(x)={:{(xe^(-(1/(|x|) + 1/x)), x ne 0),(0 , x =0 ):} then f(x) is

    Text Solution

    |

  5. If u=f(x^3),v=g(x^2),f^(prime)(x)=cosx ,a n dg^(prime)(x)=sinx ,t h e ...

    Text Solution

    |

  6. If y=((a-x)sqrt(a-x)-(b-x)sqrt(x-b))/a ,t h e n(dy)/(dx) wherever it...

    Text Solution

    |

  7. If x=(1-t^(2))/(1+t^(2)) and y=(2t)/(1+t^(2)), then (dy)/(dx) is equal...

    Text Solution

    |

  8. d/(dx)[sin^2cot^(- 1)sqrt((1-x)/(1+x))] is

    Text Solution

    |

  9. Differentiate tan^(-1)((2x)/(1-x^2)) with respect to sin^(-1)((2x)/(1+...

    Text Solution

    |

  10. If f(x) = 2 sin^(-1) sqrt(1-x) + sin^(-1)(2 sqrt(x (1-x))) where x in ...

    Text Solution

    |

  11. The derivative of sin^(-1)((2x)/(1+x^(2))) with respect to cos^(-1)((1...

    Text Solution

    |

  12. If x = sint cos2t and y = cost sin2t , then at t = pi/4, the value of ...

    Text Solution

    |

  13. If x=sectheta-costheta and y=sec^n theta- cos^n theta then show that (...

    Text Solution

    |

  14. Let y=x^3-8x+7a n dx=f(t)dot If (dy)/(dt)=2 and x=3 at t=0, then (dx)/...

    Text Solution

    |

  15. If x^y = e^(x-y) " then " dy/dx ?

    Text Solution

    |

  16. "If "y= sin x +e^(x)," then "(d^(2)x)/(dy^(2))=

    Text Solution

    |

  17. If f(x) =|log(e)|x||, then f'(x) equals

    Text Solution

    |

  18. If f(x)=x^4tan(x^3)-x1n(1+x^2), then the value of (d^4(f(x)))/(dx^4) ...

    Text Solution

    |

  19. let y=t^(10)+1, and x=t^8+1, then (d^2y)/(dx^2) is

    Text Solution

    |

  20. If x = exp {tan^(-1)((y-x^2)/(x^2))} then dy/dx equals

    Text Solution

    |